Serena Williams arrived at this year's Wimbledon appearing to have little hope of retaining the crown that she lifted for the fourth time last summer. Even by the standards of an athlete whose career has been marked as much by mishap and misfortune as by glittering success, the past 12 months have been torrid.

Last July, just four days after beating Vera Zvonareva in the Wimbledon final in straight sets, Williams trod on a beer bottle in a Munich restaurant, injuring her foot and requiring 18 stitches. She played an exhibition match against Kim Clijsters the next day, but the injury proved more serious than was initially thought and she was unable to compete again in 2010.

Then, in late February this year, a bad situation got considerably worse: a pulmonary embolism – or blood clot – was discovered on Williams's lung, thought to be connected to the treatment she'd been receiving for her foot injury. Williams was rushed to hospital in Los Angeles (she'd attended an Elton John Aids Foundation dinner the previous evening) and thankfully survived. However, the incident resulted in a flood of speculation as to whether she would ever compete at the highest level again.

Yet just four months on, Williams is back, making effortful progress through the early rounds of this year's championship. Although clearly not at her best – her movement is sluggish and her shots lack their usual fluidity – it would be foolhardy in the extreme to write her off. After all, in a career that has spanned 16 years, the youngest Williams sister, now 29, has made a speciality of staging unlikely comebacks.

Perhaps most spectacular of all was her victory at the 2007 Australian Open, a tournament for which she turned up overweight, out of practice and ranked just 81 in the world, having spent most of the previous three years away from the game, battling the depression that engulfed her following the murder of her older sister Yetunde in 2003. Few then gave her any chance at all – yet she ended up thrashing Maria Sharapova in the final. Who's to say something similar won't happen in six days' time? Williams's attention-grabbing reappearance at this year's Wimbledon, together with her big sister Venus (also out for most of the past year with injuries), is a reminder of something else about the Williams sisters, and Serena in particular – that controversy and drama invariably follow in their wake.

Already at this year's tournament, Serena has hit the headlines both for straightforwardly positive reasons (her tearful reaction to beating Aravane Rezai in the first round) and for less edifying ones. A conspiracy theory has been doing the rounds relating to her foot injury in Munich: the restaurant where the incident happened has apparently never been identified, and some find it odd that Williams hasn't pursued a legal claim against it.

In an interview, Williams also touched on another long-standing bugbear – the supposed prejudice of the tennis authorities against her and her sister – when she made clear her displeasure at having to play one of her matches away from the show courts: "They like to put us on Court Two, me and Venus, for whatever reason. I haven't figured it out yet."

These incidents point to the fact that Serena Williams, despite her extraordinary success – she is the highest-earning female athlete in history – has always been, or always liked to see herself as, an outsider in the world of tennis.

In the most obvious sense, this is because of her colour: like her sister, she has succeeded in a sport that has traditionally been an all-white preserve. Yet quite apart from this, and arguably more importantly, it is because she comes from such a singular family, one containing not one but two tennis champions. There have been examples of successful siblings in sport before – the Neville brothers in football, the Bryan brothers in men's tennis – but none have come close to matching the achievements of the Williams sisters.

The story of how Richard Williams dreamt that his two daughters would be tennis stars and proceeded to make it happen is so familiar as to have taken on the quality of myth, but it is worth repeating, because it is so strange.

Serena was a toddler when her dad watched a match on TV and heard the commentator saying that a player had earned $40,000 in a single week. Amazed by this sum, Richard, who worked for a security firm, determined that he would devote himself to turning at least one of his daughters into a champion.

The family lived in Compton, a violent and impoverished LA neighbourhood. Alongside Venus and Serena, Richard's wife Oracene had three daughters from a previous marriage. The five girls all slept together in a single room. There were only four beds, so Serena had to share with a different sister each night – something that made her feel "lucky, because it gave me a chance to get real close to each of my sisters".

In her 2009 memoir, Queen of the Court, Serena describes how the family would head down en masse to the litter-strewn public courts in Lynwood, and practice their games, "sometimes hearing guns going off from drive-by shootings nearby".

Richard and Oracene had never played tennis before they started teaching their daughters, so they themselves had to pick it up from scratch. Just over a year younger than Venus, Serena was from the start a promising but not spectacular player: Venus was the real star, the one tipped for greatness. "She cast a big shadow, I'll say that," Serena writes in her memoir. "She was taller, prettier, quicker, more athletic. And she was certainly nicer. There was no living up to her."

Serena, though, not only lived up to her sister: she went on to become better than her. Though Venus has won more Wimbledon trophies (five to Serena's four), the younger sister has won more grand slams overall (13 to Venus's seven), and leads their head-to-head 13 to 10. On her day, few doubt that Serena is the stronger player, with her fierce ground shots and destructively powerful serve. In fact, she is arguably the best women tennis player of all time.

Yet in other senses Serena has remained very much the younger sister. Whereas Venus maintains a controlled, queenly bearing both on and off court, Serena is more volatile, and can come across as immature. At the 2009 US Open, she rounded on a line judge who foot-faulted her at a crucial point, shouting: "I swear to God, I'll fucking take the ball and shove it down your fucking throat." (She was fined £175,000, which she still maintains is unfair.) She has also been more drawn than her sister to non-tennis activities, including launching a fashion range and trying her hand at acting and screenwriting.

Serena also appeared more deeply affected than Venus by their sister's death in 2003. Yetunde was killed in a drive-by shooting; her boyfriend at the time was a gangster, and the bullets were intended for him. Serena has spoken of how Yetunde had always been a motivational figure for her, encouraging her to believe, even as a young girl, that she could be better than Venus.

After her death, Serena tried at first to continue playing, but then slid into a deep depression, at one point not leaving her house for weeks. Eventually, this battle with grief proved a kind of watershed. As well as embarking on therapy, Serena travelled to Africa to seek out her family's roots, visiting the slave castles and opening a school in Kenya. She realised that if she went back to tennis, it had to be because she really wanted to, not simply to please others. Her faith in God – like her mother and Venus, she is a devout Jehovah's Witness – also proved a bedrock during this period.

Serena, then, knows better than anyone what it means to claw her way back from the brink. If she does return to her winning ways again – whether in the coming week or at some future tournament – it would be yet another belief-defying chapter in a story of sporting glory that resonates far beyond tennis.